Semistability of Amalgamated Products and HNN-Extensions
Michael L. Mihalik · Steven Thomas Tschantz
Jan 1992 · American Mathematical Society: Memoirs of the American Mathematical Society Book 471 · American Mathematical Soc.
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In the study of the proper homotopy theory of finitely presented groups, semistability at infinity is an end invariant of central importance. A finitely presented group which is semistable at infinity has a well-defined fundamental group at infinity independent of base ray. In this memoir, the authors show that amalgamated products and HNN-extensions of finitely presented semistable at infinity groups are also semistable at infinity. A major step toward determining whether all finitely presented groups are semistable at infinity, this result easily generalizes to finite graphs of groups.
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